messages listlengths 1 1 | ground_truth stringlengths 1 5 | dataset stringclasses 1
value |
|---|---|---|
[
{
"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[-1, 0, 2, -2],\n [2, -3, 3, -1],\n [3, 3, 1, -4],\n [2, 0, -2, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 354 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the sum of all entries of the result:\nA =\n[[-4, 3, -4, -1],\n [0, 2, -1, -1],\n [0, 2, -3, -1],\n [-1, 1, -4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1104 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[0, 1, 0, 0],\n [1, -4, 0, -2],\n [0, 0, 2, 0],\n [0, -2, 0, -1]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 939 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the value at position (3, 2) of the result:\nA =\n[[-3, 4, -2, -2],\n [4, -1, 0, 0],\n [-2, 0, -1, -2],\n [-2, 0, -2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -496 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[4, -3, -1, 3],\n [-1, -4, 1, 4],\n [2, -2, -3, 0],\n [-1, -1, 2, 2]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 390 | MATH |
[
{
"content": "Find the sum of all entries of the 3th power of the matrix:\n[[-4, 2, 1, 0],\n [-4, 0, -2, 1],\n [3, 0, -3, 3],\n [0, 1, 2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 34 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[-3, 2, 0, 0],\n [2, -1, -2, -2],\n [0, -2, -4, 0],\n [0, -2, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 5410 | MATH |
[
{
"content": "Calculate the matrix power A^3 and find the value at position (4, 2) of the result:\nA =\n[[-4, 1, -3, 0],\n [-2, 1, -2, -4],\n [0, 0, -4, 0],\n [-2, 1, -3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[4, 0, 3, -2],\n [0, 2, 3, -1],\n [3, 3, -3, -4],\n [-2, -1, -4, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2841 | MATH |
[
{
"content": "Calculate the matrix power A^3 and find the sum of absolute values of all entries of the result:\nA =\n[[4, 4, 0, -4],\n [4, 1, 0, 0],\n [0, 0, 2, 0],\n [-4, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1473 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the value at position (3, 3) of the result:\nA =\n[[-2, 0, 2, 0],\n [0, -3, 2, -1],\n [2, 2, 0, -2],\n [0, -1, -2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 276 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[2, 0, 0, 2],\n [0, -1, -4, 2],\n [0, -4, 0, 0],\n [2, 2, 0, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 573 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^4 where A is:\n[[0, -3, 3, -4],\n [-1, -1, -2, -1],\n [2, -3, 2, 3],\n [-2, 2, 0, 1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2610 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[-4, 1, 1, -4],\n [1, -2, 2, -2],\n [1, 2, -1, 0],\n [-4, -2, 0, -1]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1023 | MATH |
[
{
"content": "Calculate the matrix power A^3 and find the sum of absolute values of all entries of the result:\nA =\n[[0, 0, 0, 0],\n [0, 2, -2, -3],\n [0, -2, 4, -4],\n [0, -3, -4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 904 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[2, 2, -2, 0],\n [2, -4, 0, -2],\n [-2, 0, -2, 0],\n [0, -2, 0, 3]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 477 | MATH |
[
{
"content": "Find the value at position (4, 2) of the 4th power of the matrix:\n[[-3, 1, -2, -2],\n [1, 0, 2, -3],\n [-2, 2, -3, 0],\n [-2, -3, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 133 | MATH |
[
{
"content": "Calculate the matrix power A^3 and find the sum of all entries of the result:\nA =\n[[2, 3, 1, -2],\n [0, 0, -3, -3],\n [0, -2, -3, 3],\n [-2, -1, 1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -120 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[-1, 3, 3, -2],\n [1, -3, -1, -2],\n [2, -3, 3, -1],\n [-3, 4, 2, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -400 | MATH |
[
{
"content": "Calculate the matrix power A^3 and find the value at position (4, 1) of the result:\nA =\n[[3, 0, -2, -2],\n [0, 4, -2, 3],\n [-2, -2, -1, 0],\n [-2, 3, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -48 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[1, 2, 2, -1],\n [2, 0, 0, 4],\n [2, 0, 0, 2],\n [-1, 4, 2, 3]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 5136 | MATH |
[
{
"content": "What is the value at position (2, 1) of the matrix A^3 where A is:\n[[-4, -4, -4, 1],\n [4, 3, -2, 3],\n [0, 2, 4, -4],\n [1, -4, 3, 1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -64 | MATH |
[
{
"content": "What is the value at position (4, 3) of the matrix A^3 where A is:\n[[4, 3, -2, 2],\n [3, 2, -4, 1],\n [-2, -4, 0, -3],\n [2, 1, -3, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -207 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the value at position (4, 2) of the result:\nA =\n[[-4, 2, 1, 1],\n [-1, 1, 0, -1],\n [2, 1, -3, 0],\n [3, 4, 1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 80 | MATH |
[
{
"content": "Find the value at position (1, 2) of the 4th power of the matrix:\n[[0, 1, -1, 0],\n [-1, 4, 0, 1],\n [3, -2, 1, -1],\n [1, -3, 2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 46 | MATH |
[
{
"content": "Find the sum of all entries of the 4th power of the matrix:\n[[-2, 1, -1, 2],\n [1, 1, 0, 0],\n [-1, 0, 3, -1],\n [2, 0, -1, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 63 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 3th power of the matrix:\n[[-2, 0, -1, 0],\n [0, -3, 2, 0],\n [-1, 2, -1, 2],\n [0, 0, 2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 333 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the sum of all entries of the result:\nA =\n[[1, 0, 0, 4],\n [4, 1, -4, 1],\n [4, -2, 4, -3],\n [2, -4, -3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2070 | MATH |
[
{
"content": "Find the sum of all entries of the 4th power of the matrix:\n[[-3, 0, -2, -4],\n [-4, 0, 2, 2],\n [-3, 3, -1, 0],\n [2, -1, -4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 299 | MATH |
[
{
"content": "Calculate the matrix power A^3 and find the value at position (3, 2) of the result:\nA =\n[[0, 2, -1, -4],\n [1, -3, -4, 1],\n [2, 4, 0, -1],\n [-3, -4, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -46 | MATH |
[
{
"content": "Calculate the matrix power A^3 and find the sum of all entries of the result:\nA =\n[[2, -1, 1, 4],\n [-1, -1, -1, 3],\n [-1, 2, 2, 0],\n [2, -1, 1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 128 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the sum of absolute values of all entries of the result:\nA =\n[[3, 3, -3, 0],\n [4, 0, -2, -2],\n [0, -3, 2, 3],\n [1, 0, -4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4803 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[0, -1, 1, 3],\n [-3, -2, 0, 4],\n [-1, 1, 2, 0],\n [4, 3, -1, 2]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2018 | MATH |
[
{
"content": "Calculate the matrix power A^3 and find the sum of all entries of the result:\nA =\n[[-1, 0, -2, 0],\n [0, 2, 2, 0],\n [-2, 2, -4, 4],\n [0, 0, 4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 15 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[-2, 2, 0, 3],\n [2, -3, -2, 0],\n [0, -2, 2, 1],\n [3, 0, 1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3252 | MATH |
[
{
"content": "Find the sum of all entries of the 3th power of the matrix:\n[[-2, 0, 1, -4],\n [0, -3, 2, 1],\n [1, 2, -2, -3],\n [-4, 1, -3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -214 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[-3, 0, -3, -1],\n [1, 3, 2, -3],\n [0, 1, -2, -1],\n [1, 4, -2, 3]], determine the value at position (4, 2).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 61 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[-2, 1, -4, -4],\n [-1, -3, -4, -1],\n [1, -2, 4, 2],\n [-4, 4, 0, 3]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 876 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[0, -4, -1, 1],\n [-4, 2, 2, 4],\n [-1, 2, 3, 2],\n [1, 4, 2, 2]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 19289 | MATH |
[
{
"content": "What is the value at position (1, 1) of the matrix A^3 where A is:\n[[-4, 2, 0, 1],\n [2, -3, 2, -2],\n [0, 2, -4, -2],\n [1, -2, -2, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -122 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[1, 1, 2, 0],\n [1, 4, -3, 4],\n [2, -3, 0, -1],\n [0, 4, -1, -3]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1078 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the value at position (2, 4) of the result:\nA =\n[[2, 0, 2, -3],\n [0, 1, 0, 0],\n [2, 0, 0, 1],\n [-3, 0, 1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^3 where A is:\n[[-3, -3, -4, 0],\n [2, -2, -3, 3],\n [3, 0, 4, 4],\n [-4, -3, 1, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1399 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[-2, 3, 1, -2],\n [3, -4, -3, 0],\n [1, -3, 1, -2],\n [-2, 0, -2, -3]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 8852 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[0, 3, -2, 2],\n [2, -1, -1, -3],\n [4, -2, 3, -3],\n [3, -2, 0, -1]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 706 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[-1, 2, 4, 0],\n [2, 2, -1, -2],\n [4, -1, -1, 0],\n [0, -2, 0, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 514 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[-4, 2, 0, 2],\n [2, 0, 0, -2],\n [0, 0, -3, -1],\n [2, -2, -1, 0]], determine the value at position (2, 2).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -32 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the value at position (4, 3) of the result:\nA =\n[[3, 0, 4, 3],\n [0, -4, 0, 3],\n [2, 0, -4, -3],\n [-4, 2, 2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -250 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the sum of absolute values of all entries of the result:\nA =\n[[3, -2, 0, 0],\n [-3, -4, 2, -4],\n [1, 4, 4, 3],\n [-3, 3, 3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 5176 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the sum of absolute values of all entries of the result:\nA =\n[[-2, -3, 3, -3],\n [-1, -4, 2, 3],\n [3, 2, -4, -2],\n [-3, 1, 1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 14893 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^3 where A is:\n[[-2, 1, -2, 1],\n [1, 1, 0, 2],\n [-2, 0, -4, 4],\n [1, 2, 4, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 220 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[-1, -1, -3, -1],\n [-1, -2, 0, 4],\n [-3, 0, 4, 2],\n [-1, 4, 2, 0]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1144 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[-1, 0, 2, 0],\n [0, -4, 0, -1],\n [2, 0, 4, 1],\n [0, -1, 1, 0]], determine the value at position (2, 2).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 306 | MATH |
[
{
"content": "Find the value at position (1, 3) of the 3th power of the matrix:\n[[-2, 0, -3, -1],\n [0, -4, 0, -4],\n [-3, 0, -4, 2],\n [-1, -4, 2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -120 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^3 where A is:\n[[3, 0, 2, 0],\n [0, 1, 0, 2],\n [2, 0, 3, -4],\n [0, 2, -4, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1017 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[4, -2, 1, -2],\n [-2, -2, -2, 0],\n [1, -2, 3, 0],\n [-2, 0, 0, -4]], determine the value at position (2, 3).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -42 | MATH |
[
{
"content": "Calculate the matrix power A^3 and find the value at position (3, 4) of the result:\nA =\n[[-2, -3, -2, 3],\n [2, -1, 0, 4],\n [1, 4, -3, 2],\n [0, 2, 3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -45 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^3 where A is:\n[[-3, 4, -1, -2],\n [-1, -3, -1, -2],\n [-3, 1, 4, 2],\n [2, -2, -1, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 7 | MATH |
[
{
"content": "What is the value at position (4, 4) of the matrix A^3 where A is:\n[[-4, 4, 2, -2],\n [1, 2, -4, 2],\n [4, -2, 4, 0],\n [3, -3, 0, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -3 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^3 where A is:\n[[2, -2, 3, 0],\n [0, -4, -2, -4],\n [-3, 3, -3, 2],\n [3, 1, 4, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 266 | MATH |
[
{
"content": "Calculate the matrix power A^3 and find the sum of all entries of the result:\nA =\n[[-1, -3, 3, 0],\n [-3, 2, -2, 2],\n [3, -2, 3, 3],\n [0, 2, 3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 492 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the sum of absolute values of all entries of the result:\nA =\n[[4, 3, -1, -4],\n [4, -4, 1, -2],\n [3, 3, -2, 3],\n [3, 1, 1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4536 | MATH |
[
{
"content": "What is the value at position (3, 1) of the matrix A^4 where A is:\n[[-1, 2, 3, -4],\n [-3, 1, -3, 4],\n [-1, 1, -2, -1],\n [4, 3, 3, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -158 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[-4, 0, -3, 0],\n [0, 0, 0, 2],\n [-3, 0, 3, 2],\n [0, 2, 2, 0]], determine the value at position (4, 4).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 12 | MATH |
[
{
"content": "Find the sum of all entries of the 3th power of the matrix:\n[[4, 2, 3, -3],\n [-1, 2, 3, 4],\n [0, -1, -3, 1],\n [0, 4, 2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 741 | MATH |
[
{
"content": "Find the value at position (3, 2) of the 4th power of the matrix:\n[[-4, 2, 0, -2],\n [2, -3, 0, 0],\n [0, 0, -1, -1],\n [-2, 0, -1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -36 | MATH |
[
{
"content": "Calculate the matrix power A^3 and find the sum of absolute values of all entries of the result:\nA =\n[[1, 2, -2, -1],\n [2, -3, 0, 1],\n [-2, 0, -1, -4],\n [-1, 1, -4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1276 | MATH |
[
{
"content": "Find the value at position (2, 4) of the 4th power of the matrix:\n[[-1, -2, 0, -2],\n [-2, -4, -3, 0],\n [0, -3, 2, 0],\n [-2, 0, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 128 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[0, -3, 2, 3],\n [-2, -1, -3, -1],\n [-3, 1, -4, -4],\n [2, 2, -1, 1]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 344 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the sum of absolute values of all entries of the result:\nA =\n[[2, 2, -3, 0],\n [2, -4, 1, -2],\n [-3, 1, 2, 0],\n [0, -2, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4445 | MATH |
[
{
"content": "Find the sum of all entries of the 4th power of the matrix:\n[[-4, 0, -2, 0],\n [0, 1, 2, 2],\n [-2, 2, -2, 0],\n [0, 2, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2785 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the sum of all entries of the result:\nA =\n[[-2, -3, 3, -3],\n [-2, -1, -1, -3],\n [4, -2, 3, 1],\n [-2, -3, 3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 11199 | MATH |
[
{
"content": "What is the value at position (4, 3) of the matrix A^4 where A is:\n[[1, 2, 4, 2],\n [2, 0, 0, 0],\n [4, 0, 3, 0],\n [2, 0, 0, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 296 | MATH |
[
{
"content": "Find the sum of all entries of the 4th power of the matrix:\n[[1, 4, 2, -2],\n [4, -3, 0, -2],\n [2, 0, 4, -2],\n [-2, -2, -2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2982 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[-3, 2, 4, -1],\n [2, 2, 4, 1],\n [2, -3, 1, 2],\n [1, -3, -2, 4]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -1851 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[1, 0, 0, 2],\n [0, 4, 0, -2],\n [0, 0, -2, 0],\n [2, -2, 0, -2]], determine the value at position (4, 4).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -20 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 3th power of the matrix:\n[[3, -4, -1, -2],\n [-4, -1, 4, -2],\n [-4, 1, 2, -1],\n [3, -1, -4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2175 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[-2, -4, -4, 1],\n [-2, 1, -3, -4],\n [-4, 1, -3, 0],\n [-1, 3, 1, -3]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 6951 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[-3, 0, 3, -1],\n [0, 3, 1, 2],\n [3, 1, 4, 2],\n [-1, 2, 2, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 7955 | MATH |
[
{
"content": "Find the value at position (2, 1) of the 4th power of the matrix:\n[[4, -1, -1, -1],\n [0, 0, 2, -3],\n [-2, 1, 4, 0],\n [-4, 3, -2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -128 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[4, 0, -2, 3],\n [0, -4, 2, 2],\n [-2, 2, -2, -2],\n [3, 2, -2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 8645 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[0, 0, -2, 3],\n [0, 2, -2, -2],\n [-2, -2, -1, -3],\n [3, -2, -3, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1461 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the sum of all entries of the result:\nA =\n[[-4, -4, 0, -2],\n [-4, -2, -4, -2],\n [0, -4, 1, 1],\n [-2, -2, 1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 16621 | MATH |
[
{
"content": "What is the value at position (1, 2) of the matrix A^4 where A is:\n[[-4, -2, -4, -2],\n [-2, -1, 0, -4],\n [-4, 0, 3, 2],\n [-2, -4, 2, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1090 | MATH |
[
{
"content": "Calculate the matrix power A^3 and find the sum of absolute values of all entries of the result:\nA =\n[[-4, 2, 3, 4],\n [-3, 1, -1, -3],\n [2, 4, 1, 4],\n [3, 4, -4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1533 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 3th power of the matrix:\n[[-1, -2, -1, -2],\n [-2, 3, 0, 0],\n [-1, 0, -1, -3],\n [-2, 0, -3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 500 | MATH |
[
{
"content": "Find the value at position (2, 2) of the 3th power of the matrix:\n[[4, 4, 2, 0],\n [1, 1, -2, 4],\n [-2, -1, -3, 1],\n [4, 0, -1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 105 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the sum of absolute values of all entries of the result:\nA =\n[[2, -2, 2, -2],\n [-2, -3, 0, -1],\n [2, 0, 2, 2],\n [-2, -1, 2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2336 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[0, -3, -2, 0],\n [-3, -1, 3, -1],\n [-2, 3, -2, 1],\n [0, -1, 1, 4]], determine the value at position (4, 3).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 18 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[4, 4, 3, -2],\n [-3, -2, -2, -1],\n [3, -1, 0, -1],\n [2, 0, 1, -1]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 640 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[-3, -3, 1, 0],\n [-3, 0, 1, 0],\n [1, 1, -3, 0],\n [0, 0, 0, 3]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 527 | MATH |
[
{
"content": "Find the value at position (4, 3) of the 3th power of the matrix:\n[[3, 1, 0, -1],\n [1, 4, 0, -2],\n [0, 0, 2, 3],\n [-1, -2, 3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 63 | MATH |
[
{
"content": "Calculate the matrix power A^3 and find the value at position (3, 4) of the result:\nA =\n[[4, -2, 0, 0],\n [-2, 1, -2, -2],\n [0, -2, 0, 2],\n [0, -2, 2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 58 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[3, 2, -2, -3],\n [2, -2, 2, 0],\n [-2, 2, 1, 0],\n [-3, 0, 0, -4]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -195 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 3th power of the matrix:\n[[-2, -2, 0, -2],\n [-2, 0, -3, 1],\n [0, -3, -3, 0],\n [-2, 1, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 522 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the value at position (1, 2) of the result:\nA =\n[[-1, 4, 1, 2],\n [-3, -2, 0, 1],\n [2, -1, 1, -1],\n [-1, 0, -3, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 190 | MATH |
[
{
"content": "Calculate the matrix power A^3 and find the sum of all entries of the result:\nA =\n[[1, -3, 3, -2],\n [-2, -2, -4, -3],\n [-3, 2, 4, 2],\n [-1, 4, 2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -70 | MATH |
[
{
"content": "What is the value at position (4, 2) of the matrix A^4 where A is:\n[[2, -2, -1, 0],\n [-2, -3, 2, 0],\n [-1, 2, -3, 2],\n [0, 0, 2, 1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 128 | MATH |
[
{
"content": "Calculate the matrix power A^3 and find the sum of absolute values of all entries of the result:\nA =\n[[2, 3, 2, 0],\n [2, -4, 3, 3],\n [4, 3, 4, -1],\n [-2, 3, -3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2620 | MATH |
[
{
"content": "Find the value at position (4, 2) of the 3th power of the matrix:\n[[-4, -2, 0, 2],\n [-2, -4, 0, 1],\n [0, 0, 4, 2],\n [2, 1, 2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 109 | MATH |
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